Concurrent constraint logic programming: Difference between revisions
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{{quantum}} | |||
The '''Calogero conjecture'''<ref name="gaeta_1">Gaeta, Giuseppe. (2000). "On the cosmological implications of the Calogero conjecture" Retrieved on 26 August 2007 from [http://citeseer.ist.psu.edu/rd/14277273,431116,1,0.25,Download/http://citeseer.ist.psu.edu/cache/papers/cs/21700/http:zSzzSzwww.ma.utexas.eduzSzmp_arczSzczSz00zSz00-282.pdf/on-the-cosmological-implications.pdf XiteSeer] University of Rome ''La Sapienza''</ref> is a [[minority interpretations of quantum mechanics|minority interpretation of quantum mechanics]]. It is a [[Quantization (physics)|quantization]] explanation involving [[quantum mechanics]], originally stipulated in 1997 and further republished in 2004<ref>Calogero, Francesco. (1997) "''Cosmic origin of quantization''" Retrieved on 26 August 2007 from [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVM-3SPGX50-4T&_user=10&_coverDate=04%2F21%2F1997&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=1c7a86700cc7dbbcc4169f55d687d309 ScienceDirect] Physics Letters A, Volume 228 p335-346</ref><ref name="calo_2004">Calogero, Francesco. (2004) "''Cosmic origin of quantization''" Retrieved on 26 August 2007 from [http://www.worldscinet.com/ijmpb/18/1804n05/S0217979204024136.html WorldSciNet]. [[International Journal of Modern Physics B]], Vol. 18, Nos. 4-5 (2004) 519-525.</ref> by [[Francesco Calogero]] that suggests the classical stochastic background field to which [[Edward Nelson]] attributes quantum mechanical behavior in his theory of [[stochastic quantization]] is a fluctuating space-time, and that there are further mathematical relations between the involved quantities. | |||
The hypothesis itself suggests that if the [[angular momentum]] associated with a stochastic tremor<ref name="calo_2004" /> with [[Coherence (physics)#Spatial coherence|spatial coherence]] provides an action purported by that motion within the order of magnitude of [[Max Planck|Planck]]'s [[Planck constant|constant]]<ref name="calo_2004" /> then the order of magnitude of the associated angular momentum has the same value.<ref name="calo_2004" /> Calogero himself suggests<ref name="calo_2004" /> that these findings, originally based on the simplified model of the universe<ref name="calo_2004" /> "are affected (and essentially, unaffected) by the possible presence in the mass of the Universe of a large component made up of particles much lighter than nucleons".<ref name="calo_2004" /> | |||
Essentially, the relation explained by Calogero can be expressed with the formulas: | |||
:<math>h \approx \alpha G^{1/2} m^{3/2} [R(t)]^{1/2}.</math> | |||
Furthermore: | |||
:<math>h \equiv h(t) = A \sqrt{R(t)} = h_0 \sqrt{a(t)}</math> Const G,m | |||
Where: | |||
:<math>G</math> represents the [[gravitational constant]] | |||
:<math>m</math> represents the mass of a hydrogen atom. | |||
:<math>R(t)</math> represents the radius of the universe accessible by gravitational interactions in time, t. | |||
:<math>A</math> is a dimensional constant. | |||
Despite its common description, it has been noted that the conjecture is not entirely defined within the realms of Nelson's stochastic mechanics, but can also be thought of as a means of inquiring into the statistical effects of interaction with distant masses in the universe and was expected by Calogero himself<ref name="gaeta_1" /> to be within the same order of magnitude as quantum mechanical effects.<ref name="gaeta_1" /> | |||
== Analysis == | |||
=== Compatibility with fundamental constants === | |||
<!-- A note to the foolish denouement of human consciousness, vis-a-vis notability, that there is a very limited amount of literature on this conjecture, and this definitive paper is the only one available which analyzes it in such a way. --> | |||
After the publication of Calogero's original paper, "[The] [c]osmic origin of quantization" a response was published by Giuseppe Gaeta of the [[University of Rome La Sapienza|University of Rome]]<ref name="gaeta_1" /> in which he discussed the compatibility of the conjecture with present bounds on variation of fundamental constants, but also outlined his focus on the modification of the relation between [[redshift]] and distance,<ref name="gaeta_1" /> and of the estimations attained from observations of elapsed time from the production of cosmic radiation and implications<ref name="gaeta_1" />—both being related also, to the observed [[Black body|blackbody distribution]] of background cosmic radiation.<ref name="gaeta_1" /> | |||
== References == | |||
=== Notes === | |||
{{reflist|2}} | |||
=== Journals === | |||
* F. Calogero, "''Cosmic origin of quantization''", Phys. Lett. A 228 (1997), 335-346. [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVM-3SPGX50-4T&_user=10&_coverDate=04%2F21%2F1997&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=1c7a86700cc7dbbcc4169f55d687d309] | |||
* G. Gaeta "''Calogero Conjecture and Hubble Law''", International Journal of Theoretical Physics, Vol 39 (5), May 2000, pp. 1339–1350(12) [http://www.ingentaconnect.com/content/klu/ijtp/2000/00000039/00000005/00224257;jsessionid=1k7xkfasad208.alice?format=bib] | |||
* G. Gaeta "''On the cosmological implications of the Calogero conjecture''" [http://citeseer.ist.psu.edu/431116.html] | |||
[[Category:Quantum mechanics]] | |||
[[Category:Conjectures]] | |||
Revision as of 18:11, 3 June 2013
Template:Quantum The Calogero conjecture[1] is a minority interpretation of quantum mechanics. It is a quantization explanation involving quantum mechanics, originally stipulated in 1997 and further republished in 2004[2][3] by Francesco Calogero that suggests the classical stochastic background field to which Edward Nelson attributes quantum mechanical behavior in his theory of stochastic quantization is a fluctuating space-time, and that there are further mathematical relations between the involved quantities.
The hypothesis itself suggests that if the angular momentum associated with a stochastic tremor[3] with spatial coherence provides an action purported by that motion within the order of magnitude of Planck's constant[3] then the order of magnitude of the associated angular momentum has the same value.[3] Calogero himself suggests[3] that these findings, originally based on the simplified model of the universe[3] "are affected (and essentially, unaffected) by the possible presence in the mass of the Universe of a large component made up of particles much lighter than nucleons".[3]
Essentially, the relation explained by Calogero can be expressed with the formulas:
![h\approx \alpha G^{{1/2}}m^{{3/2}}[R(t)]^{{1/2}}.](https://wikimedia.org/api/rest_v1/media/math/render/svg/e29e22f170d73d0c2dc02adc0627b0837b938bb9)
Furthermore:
- Const G,m
Where:
- represents the gravitational constant
- represents the mass of a hydrogen atom.
- represents the radius of the universe accessible by gravitational interactions in time, t.
- is a dimensional constant.
Despite its common description, it has been noted that the conjecture is not entirely defined within the realms of Nelson's stochastic mechanics, but can also be thought of as a means of inquiring into the statistical effects of interaction with distant masses in the universe and was expected by Calogero himself[1] to be within the same order of magnitude as quantum mechanical effects.[1]
Analysis
Compatibility with fundamental constants
After the publication of Calogero's original paper, "[The] [c]osmic origin of quantization" a response was published by Giuseppe Gaeta of the University of Rome[1] in which he discussed the compatibility of the conjecture with present bounds on variation of fundamental constants, but also outlined his focus on the modification of the relation between redshift and distance,[1] and of the estimations attained from observations of elapsed time from the production of cosmic radiation and implications[1]—both being related also, to the observed blackbody distribution of background cosmic radiation.[1]
References
Notes
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Journals
- F. Calogero, "Cosmic origin of quantization", Phys. Lett. A 228 (1997), 335-346. [1]
- G. Gaeta "Calogero Conjecture and Hubble Law", International Journal of Theoretical Physics, Vol 39 (5), May 2000, pp. 1339–1350(12) [2]
- G. Gaeta "On the cosmological implications of the Calogero conjecture" [3]
- ↑ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 Gaeta, Giuseppe. (2000). "On the cosmological implications of the Calogero conjecture" Retrieved on 26 August 2007 from XiteSeer University of Rome La Sapienza
- ↑ Calogero, Francesco. (1997) "Cosmic origin of quantization" Retrieved on 26 August 2007 from ScienceDirect Physics Letters A, Volume 228 p335-346
- ↑ 3.0 3.1 3.2 3.3 3.4 3.5 3.6 Calogero, Francesco. (2004) "Cosmic origin of quantization" Retrieved on 26 August 2007 from WorldSciNet. International Journal of Modern Physics B, Vol. 18, Nos. 4-5 (2004) 519-525.